Representations Of Reductive Groups Over Finite Local Rings Of Length Two

Let F q be a finite field of characteristic p, and let W 2 (F q ) be the ring of Witt vectors of length two over F q . We prove that for any reductive group scheme G over Z such that p is very good for G×F q , the groups G(F q [t]/t 2 ) and G(W 2 (F q )) have the same number of irreducible representations of dimension d, for each d. Equivalently, there exists an isomorphism of group algebras C[G(F q [t]/t 2 )]≅C[G(W 2 (F q ))].